Dynamical system analysis of FLRW models with Modified Chaplygin gas

We investigate Friedmann–Lamaitre–Robertson–Walker (FLRW) models with modified Chaplygin gas and cosmological constant, using dynamical system methods. We assume [Formula: see text] as equation of state where [Formula: see text] is the matter-energy density, p is the pressure, [Formula: see text] is a parameter which can take on values [Formula: see text] as well as A and [Formula: see text] are positive constants. We draw the state spaces and analyze the nature of the singularity at the beginning, as well as the fate of the universe in the far future. In particular, we address the question whether there is a solution which is stable for all the cases.